



U = / pu dz- , V = / pv dz 

 -D -D 



Since the integration is carried out from a depth where the total 



motion is zero (u = v = w = 0), to the surface, (z = 0)*, it follows 



from (3) that 



Jj J pu dz + |^ / pv dz = , 



-D 

 and that 



div M 



V 



Equation (4) states that the horizontal divergence of the 

 total mass transport equals zero, in contrast to the divergence 

 of the mass transport in individual levels. For example in the 

 layer of frictional influence (wind drift current), the divergence 

 may be zero in exceptional cases only. 



The special form of the equation of continuity for the verti- 

 cally integrated mass transport (4) permits the introduction of a 

 "stream function", \|/ , for the mass transport, and 



U = dv///dy 

 v = - tf\|//dx 

 Integration of equations (1) over the depth between the level of 



no motion (z = -D) and the surface (z = 0) gives 



-° ,2. 



y_ D oz 

 y_ D oz 



(6) 



* Actually z = £ , where £ the elevation or depression of the sea 

 surface with reference to the level surface of the undisturbed sea 

 surface. However, since {, is a very small quantity it can be 

 neglected against D. 



